On Church's Thesis in Cubical Assemblies
Logic
2019-05-09 v1 Logic in Computer Science
Abstract
We show that Church's thesis, the axiom stating that all functions on the naturals are computable, does not hold in the cubical assemblies model of cubical type theory. We show that nevertheless Church's thesis is consistent with univalent type theory by constructing a reflective subuniverse of cubical assemblies where it holds.
Cite
@article{arxiv.1905.03014,
title = {On Church's Thesis in Cubical Assemblies},
author = {Andrew Swan and Taichi Uemura},
journal= {arXiv preprint arXiv:1905.03014},
year = {2019}
}